JEE Mains · Maths · STD 12 - 13. probability
Let \(A\) and \(E\) be any two events with positive probabilities:
Statement \(- 1\): \(P\left( {E/A} \right) \geq P\left( {A/E} \right)P\left( E \right)\)
Statement \(-2\) : \(P\left( {A/E} \right) \geq P\left( {A \cap E} \right)\)
- A Both the statements are true
- B Both the statements are false
- C Statement \(-1\) is true, Statement \(- 2\) is false
- D Statement \(-1\) is false, Statement \(-2\) is true
Answer & Solution
Correct Answer
(A) Both the statements are true
Step-by-step Solution
Detailed explanation
Let \(A\) and \(E\) be any two events with positive probabilities. Consider statement-\(1\): \(\mathrm{P}(\mathrm{E} / \mathrm{A}) \geq \mathrm{P}(\mathrm{A} / \mathrm{E}) \mathrm{P}(\mathrm{E})\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(g ( x )=\int_{0}^{ x } f( t ) dt ,\) where \(f\) is continuous function in \([0,3]\) such that \(\frac{1}{3} \leq f(t) \leq 1\) for all \(t \in[0,1]\) and \(0 \leq f( t ) \leq \frac{1}{2}\) for all \(t \in(1,3]\) The largest possible interval in which \(g (3)\) lies is :JEE Mains 2021 Hard
- If each of the lines \(5x + 8y = 13\) and \(4x - y = 3\) contains a diameter of the circle
\(x^2 + y^2 - 2\,(a^2 - 7a + 11)\) \(x - 2\, ( a^2 - 6a + 6)\, y + b^3 + 1 = 0\), thenJEE Mains 2013 Hard - Let \(A =\{2,3,4\}\) and \(B =\{8,9,12\}\). Then the number of elements in the relation \(R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in(A \times B, A \times B): a_1\right.\) divides \(b_2\) and \(a_2\) divides \(\left.b_1\right\}\) is:JEE Mains 2023 Medium
- If the domain of the function \( f(x)=\log_{(10x^{2}-17x+7)}(18x^{2}-11x+1) \) is \( (-\infty,a)\cup(b,c)\cup(d,\infty)-\{e\} \), then \( 90(a+b+c+d+e) \) equals:JEE Mains 2026 Medium
- Let \(f : [-1,3] \to R\) be defined as \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{\left| x \right| + \left[ x \right],}&{ - 1 \leq x < 1} \\
{x + \left| x \right|,}&{1 \leq x < 2} \\
{x + \left| x \right|,}&{2 \leq x \leq 3}
\end{array}} \right.\) where \([t]\) denotes the greatest integer less than or equal to \(t\). Then, \(f\) is discontinuous at:JEE Mains 2019 Hard - Let \(y=y(x)\) be the solution curve of the differential equation \(\sin \left(2 x^{2}\right) \log _{c}\left(\tan x^{2}\right) d y+\left(4 x y-4 \sqrt{2} x \sin \left(x^{2}-\frac{\pi}{4}\right)\right) d x=0\) \(0 < x < \sqrt{\frac{\pi}{2}}\), which passes through the point \(\left(\sqrt{\frac{\pi}{6}}, 1\right)\). Then \(\left|y\left(\sqrt{\frac{\pi}{3}}\right)\right|\) is equal to \(.....\)JEE Mains 2022 Hard
More PYQs from JEE Mains
- The locus of the mid-point of the line segment joining the focus of the parabola \(y^{2}=4 a x\) to a moving point of the parabola, is another parabola whose directrix isJEE Mains 2021 Hard
- Let \(f(\mathrm{x})=\left|2 \mathrm{x}^2+5\right| \mathrm{x}|-3|, \mathrm{x} \in \mathrm{R}\). If \(\mathrm{m}\) and \(\mathrm{n}\) denote the number of points where \(f\) is not continuous and not differentiable respectively, then \(m+n\) is equal to :JEE Mains 2024 Medium
- The total number or irrational terms in the binomial expansion of \(\left( {{7^{1/5}} - {3^{1/10}}} \right)^{60}\) isJEE Mains 2019 Hard
- If the system of linear equations \(x+y+3 z=0\) \(x+3 y+k^{2} z=0\) \(3 x+y+3 z=0\) has a non-zero solution \((x, y, z)\) for some \(k \in R ,\) then \(x +\left(\frac{ y }{ z }\right)\) is equal toJEE Mains 2020 Medium
- Let \(\vec a = 2\hat i + \hat j - 2\hat k,\vec b = \hat i + \hat j\). If \(\vec c\) is a vector such that \(\vec a.\vec c = \left| {\vec c} \right|,\left| {\vec c - \vec a} \right| = 2\sqrt 2 \) and the angle between \(\vec a \times \vec b\) and \(\vec c\) is \(30^o\), then \(\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right|\) equalsJEE Mains 2013 Hard
- The distance of the point \((7,-3,-4)\) from the plane passing through the points \((2,-3,1),(-1,1,-2)\) and \((3,-4,2)\) is:JEE Mains 2023 Easy